What is the integral of (8-4x)e^{2x} ?

The integral of (8-4x)e^{2x} is -2e^{2x}x+5e^{2x}+C

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integral of (8-4x)e^{2x}

\int (8 - 4 x) e^{2 x} d x

- 2 e^{2 x} x + 5 e^{2 x} + C

Solution steps

\int (8 - 4 x) e^{2 x} d x

Apply Integration By Parts

= 2 e^{2 x} (- x + 2) - \int - 2 e^{2 x} d x

\int - 2 e^{2 x} d x = - e^{2 x}

= 2 e^{2 x} (- x + 2) - (- e^{2 x})

Simplify

2 e^{2 x} (- x + 2) - (- e^{2 x}) : - 2 e^{2 x} x + 5 e^{2 x}

= - 2 e^{2 x} x + 5 e^{2 x}

Add a constant to the solution

= - 2 e^{2 x} x + 5 e^{2 x} + C

What is the integral of (8-4x)e^{2x} ?
The integral of (8-4x)e^{2x} is -2e^{2x}x+5e^{2x}+C